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Tree-based varying coefficient regression for longitudinal ordinal responses

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  • Bürgin, Reto
  • Ritschard, Gilbert

Abstract

A tree-based algorithm for longitudinal regression analysis that aims to learn whether and how the effects of predictor variables depend on moderating variables is presented. The algorithm is based on multivariate generalized linear mixed models and it builds piecewise constant coefficient functions. Moreover, it is scalable for many moderators of possibly mixed scales, integrates interactions between moderators and can handle nonlinearities. Although the scope of the algorithm is quite general, the focus is on its usage in an ordinal longitudinal regression setting. The potential of the algorithm is illustrated by using data derived from the British Household Panel Study, to show how the effect of unemployment on self-reported happiness varies across individual life circumstances.11R-codes and datasets are available online as supplementary files (see Appendix B).

Suggested Citation

  • Bürgin, Reto & Ritschard, Gilbert, 2015. "Tree-based varying coefficient regression for longitudinal ordinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 86(C), pages 65-80.
    • Handle: RePEc:eee:csdana:v:86:y:2015:i:c:p:65-80
    DOI: 10.1016/j.csda.2015.01.003
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    References listed on IDEAS

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    1. Tutz, Gerhard & Kauermann, Goran, 2003. "Generalized linear random effects models with varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 43(1), pages 13-28, May.
    2. Donald W. K. Andrews, 2003. "Tests for Parameter Instability and Structural Change with Unknown Change Point: A Corrigendum," Econometrica, Econometric Society, vol. 71(1), pages 395-397, January.
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    7. Tutz, Gerhard & Hennevogl, Wolfgang, 1996. "Random effects in ordinal regression models," Computational Statistics & Data Analysis, Elsevier, vol. 22(5), pages 537-557, September.
    8. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    9. Xiaogang Su & Karen Meneses & Patrick McNees & Wesley O. Johnson, 2011. "Interaction trees: exploring the differential effects of an intervention programme for breast cancer survivors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 60(3), pages 457-474, May.
    10. Göran Kauermann, 2000. "Modeling Longitudinal Data with Ordinal Response by Varying Coefficients," Biometrics, The International Biometric Society, vol. 56(3), pages 692-698, September.
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    1. Gerhard Tutz & Moritz Berger, 2018. "Tree-structured modelling of categorical predictors in generalized additive regression," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 737-758, September.
    2. Spuck, Nikolai & Schmid, Matthias & Monin, Malte & Berger, Moritz, 2025. "Confidence intervals for tree-structured varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 207(C).
    3. Bürgin, Reto & Ritschard, Gilbert, 2017. "Coefficient-Wise Tree-Based Varying Coefficient Regression with vcrpart," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 80(i06).
    4. Hajjem, Ahlem & Larocque, Denis & Bellavance, François, 2017. "Generalized mixed effects regression trees," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 114-118.

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